Cantilever Beam  Theory vs Elmer results
Cantilever Beam  Theory vs Elmer results
Hello,
I am looking to determine the mass, stress and displacement of a cantilever beam subjected to horizontal and vertical loads at its free end. The theoretical model is attached with this message.
I have been using the files from tutorial 3 in the Elmer GUI Manual  Linear Elasticity/Cantilever Beam/beam3d.grd. The displacement values compare well (theory vs Elmer). How do I solve for the mass? The Linear elasticity solver solves for displacement and stress, but I couldn't find an option for mass.
Also, which of the Elmer stress (von mises/stress in xx/stress in yy, etc.) values should I compare with the theoretical stress value?
Thank you for any information you can provide.
 Anjali
I am looking to determine the mass, stress and displacement of a cantilever beam subjected to horizontal and vertical loads at its free end. The theoretical model is attached with this message.
I have been using the files from tutorial 3 in the Elmer GUI Manual  Linear Elasticity/Cantilever Beam/beam3d.grd. The displacement values compare well (theory vs Elmer). How do I solve for the mass? The Linear elasticity solver solves for displacement and stress, but I couldn't find an option for mass.
Also, which of the Elmer stress (von mises/stress in xx/stress in yy, etc.) values should I compare with the theoretical stress value?
Thank you for any information you can provide.
 Anjali
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 Cantilever Beam Theoretical Model.PNG
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Re: Cantilever Beam  Theory vs Elmer results
Your equations are calculating normal X stress so you would compare to XX. Not sure if Elmer outputs mass, total mass is not required to solve the linear static problem unless a gravity load is used. If you run a case with just a 1G body force then the reaction force is equal to the mass.
Re: Cantilever Beam  Theory vs Elmer results
Thank you for your response. Had one follow up question  in the equation there is also the Y components, so would I need to compare it with XX + YY?

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Re: Cantilever Beam  Theory vs Elmer results
After studying your equations further, the beams length must be in the Z direction, therefore the normal bending stress is ZZ. X is the width, and t is the Y direction. The horizontal load produces bending about the Y axis, and the vertical load produces bending about the X axis, both bending stresses add together at point 1 (see sketch), but the stresses are in the ZZ direction. Also your stress equation appears to assume that L = 100. Comments on weight versus mass also included in the attached. Elmer and most FEA codes use mass units not weight units.
Re: Cantilever Beam  Theory vs Elmer results
Thank you so much for sharing the derivation!
Re: Cantilever Beam  Theory vs Elmer results
Hello,
I had a follow up question. I am looking to extract force in the y direction for this problem. I tried the following in the save scalars/variable 
force 2
Force 2
force 2 Real
Force 2 Real
Stress bodyforce 2
stress bodyforce 2
For all of the above, I get the same error  "Requested variable does not exist". How can I resolve this problem?
Thank you.
 Anjali
I had a follow up question. I am looking to extract force in the y direction for this problem. I tried the following in the save scalars/variable 
force 2
Force 2
force 2 Real
Force 2 Real
Stress bodyforce 2
stress bodyforce 2
For all of the above, I get the same error  "Requested variable does not exist". How can I resolve this problem?
Thank you.
 Anjali

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 Joined: 25 Jan 2019, 01:28
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Re: Cantilever Beam  Theory vs Elmer results
I looked at the code and there is
ForceVector
LocalForce
LocalExternalForce
LoadVector
ForceVector
LocalForce
LocalExternalForce
LoadVector
Re: Cantilever Beam  Theory vs Elmer results
Hello,
Thank you for your response.
I tried the terms taht you had suggested but for some reason I am getting the same error  "Requested variable does not exist". I am not sure what I am missing.
Please find my .sif attached with this email. Thank your for your time and consideration.
 Anjali
Thank you for your response.
I tried the terms taht you had suggested but for some reason I am getting the same error  "Requested variable does not exist". I am not sure what I am missing.
Please find my .sif attached with this email. Thank your for your time and consideration.
 Anjali
 Attachments

 case.sif
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Re: Cantilever Beam  Theory vs Elmer results
Sorry I can be of no more help, the calculated variable names and output variable names are not well published for Elmer. The input variable names are in the Elmer Models manual, sometimes they are the same and sometimes they are not.

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Re: Cantilever Beam  Theory vs Elmer results
Hi
If you want to use save scalars then mass would be "operator 1 = volume" times the density. I think you can give volume "coeffcient 1 = density" to get the mass.
As forces go, you could compute stresses and the take an "boundary int" over the desired stress component. Or you could calculate the reaction forces by "Calcalate loads = True" and sum over the resulting nodal forces to get force on a boundary,
Peter
If you want to use save scalars then mass would be "operator 1 = volume" times the density. I think you can give volume "coeffcient 1 = density" to get the mass.
As forces go, you could compute stresses and the take an "boundary int" over the desired stress component. Or you could calculate the reaction forces by "Calcalate loads = True" and sum over the resulting nodal forces to get force on a boundary,
Peter